Ice sheets cling to a mountainside in northern Italy's Val D'Aosta
Four died in the first incident close to Gressony-Saint-Jean in the northern Italian Alpine region of Val d’Aosta, near the Swiss border.
They were climbing a section of a frozen waterfall when it collapsed.
The victims are thought to have plunged around 100 yards to their deaths when the large slab of ice cracked and fell away from the mountainside.
The Italian Alps
RAI television said they were all Italians and were probably experienced as it is a difficult climb.
Italian media said a fifth climber survived the tragedy because she had reached a ledge above the frozen Bonne Annee waterfall before the section fell away.
A witness who had been climbing a nearby frozen waterfall said: "We were climbing when we heard a loud roar. Shortly after we heard the helicopter."
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In a second incident, two men were killed near the town of La Grave in he French Alps when an ice sheet broke off and crashed down on them.
Julien Michon, of the mountain rescue service in Briancon, said an ice sheet broke off and crashed down on them.
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Mr Michon said the weather there was unusually warm and sunny.
The climbers' bodies were brought to Briancon.
The latest tragedies come two days after four snowboarders died in an avalanche in Tignes, in the French Alps.
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